Once dissolved, bring the mixture to a rolling boil and maintain this heat for exactly 2 minutes—this step is indispensable for achieving the proper consistency. Remove the pan from heat and immediately stir in the finely grated zest of 6 limes, which will infuse the syrup with aromatic lime oils.

Allow the syrup to cool completely to room temperature, then add the juice of 6 limes and stir thoroughly to combine. Strain the mixture through a fine sieve into a shallow freezer-proof container to remove any pulp or zest particles that might affect the texture.

Place the strained mixture in the freezer for approximately 2 hours until it reaches a mushy consistency. This intermediate freezing stage is essential, as it prevents the sorbet from becoming rock-solid and allows for proper aeration in the next step.

Once mushy, transfer the partially frozen mixture to a bowl and whisk gently to break down any ice crystals that have formed, creating a smoother texture throughout.

Complete the sorbet by incorporating the egg whites, which will give it a luxurious, creamy consistency. Whisk 2 egg whites in a separate, scrupulously clean bowl until stiff peaks form, being careful not to over-whisk until they become dry and grainy.

Gently fold the whipped egg whites into the lime mixture using a spatula, preserving as much of the aerated structure as possible. Return the sorbet to the freezer and freeze until completely firm.

When ready to serve, transfer the sorbet to the refrigerator for approximately 30 minutes to allow it to soften slightly, making it easier to scoop, then garnish with strips of lime peel.